The reason i asked about the transmission type is that if it's a powerglide there is a fix for it. I used to have to go in at a high idle to avoid backing out, I tried a bunch of parts to fix it. Now sonnex has come out with a servo kit that absolutely locks the car down when the button is pushed. The part# is 2882110K, rockauto is the cheapest place to get it.
Smart-Tech® Ratio-Style Servo Kit - 28821-10K